Finite Group Databasebeta

← #7654163

Subgroups — #7654163

Order 512.

5141 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42694C213yesmaximal, complemented
2#42660C213yesmaximal, complemented
3#42524C213yesmaximal, complemented
4#42467C213yesmaximal, complemented
5#40188C213yesmaximal, complemented
6#40174C213yesmaximal, complemented
7#40171C213yesmaximal, complemented
8#40121C213yesmaximal, complemented
9#39789C213yesmaximal, complemented
10#39411C213yesmaximal, complemented
11#39403C213yesmaximal, complemented
12#39240C213yesmaximal, complemented
13#37591C213yesmaximal, complemented
14#36583C211yesmaximal, characteristic, complemented
15#36458C211yesmaximal, characteristic, complemented
16#36458C211yesmaximal, characteristic, complemented
17#36457C211yesmaximal, characteristic, complemented
18#36456C211yesmaximal, characteristic, complemented
19#36433C211yesmaximal, characteristic, complemented
20#36433C211yesmaximal, characteristic, complemented
21#36431C211yesmaximal, characteristic, complemented
22#36049C211yesmaximal, characteristic, complemented
23#36029C211yesmaximal, characteristic
24#35937C211yesmaximal, characteristic, complemented
25#35816C211yesmaximal, characteristic, complemented
26#35198C213yesmaximal, complemented
27#35107C213yesmaximal, complemented
28#34968C213yesmaximal, complemented
29#34263C211yesmaximal, characteristic, complemented
30C4×#557C211yesmaximal, characteristic, complemented
31C4×#550C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#542C2216yes—
39C2×#520C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42#2860C2213yes—
43#2860C2213yes—
44#2858C2213yes—
45#2858C2213yes—
46#2857C2213yes—
47#2854C2213yes—
48#2854C2213yes—
49#2851C2213yes—
50#2830C2216yes—
51#2829C2216yes—
52#2800C2216yes—
53#2772C2216yes—
54#2751C2216yes—
55#2741C2216yes—
56#2737C2216yes—
57#2731C2216yes—
58#2716C2216yes—
59#2715C2216yes—
60#2712C2216yes—
61#2705C2216yes—
62#2702C2216yes—
63#2701C2216yes—
64#2700C2216yes—
65#2691C2216yes—
66#2686C2216yes—
67#2672C2216yes—
68#2662C2216yes—
69#2662C2216yes—
70#2662C2216yes—
71#2660C2213yes—
72#2651C2216yes—
73#2650C2216yes—
74#2641C2213yes—
75#2638C2216yes—
76#2630C2216yes—
77#2630C2216yes—
78#2629C2213yes—
79#2619C2213yes—
80#2584C2213yes—
81#2580C2213yes—
82#2566C2213yes—
83#2566C2213yes—
84#2563C2213yes—
85#2563C2213yes—
86#2562C2213yes—
87#2551C2213yes—
88#2551C2213yes—
89#2550C2213yes—
90#2550C2213yes—
91#2548C2213yes—
92#2548C2213yes—
93#2548C2213yes—
94#2547C2213yes—
95#2546C2213yes—
96#2541C2213yes—
97#2538C2213yes—
98#2538C2213yes—
99#2535C2213yes—
100#2525C2213yes—
101#2525C2213yes—
102#2521C2213yes—
103#2521C2213yes—
104#2520C2211yescharacteristic
105#2520C2213yes—
106#2515C2213yes—
107#2515C2213yes—
108#2513C2213yes—
109#2513C2213yes—
110#2512C2213yes—
111#2512C2213yes—
112#2512C2213yes—
113#2512C2213yes—
114#2500C2213yes—
115#2500C2213yes—
116#2497C2213yes—
117#2497C2213yes—
118#2496C2213yes—
119#2496C2213yes—
120#2495C2213yes—
121#2495C2213yes—
122#2491C2213yes—
123#2491C2213yes—
124#2491C2216yes—
125#2491C2213yes—
126#2491C2213yes—
127#2491C2213yes—
128#2491C2213yes—
129#2490C2213yes—
130#2490C2213yes—
131#2490C2213yes—
132#2490C2213yes—
133#2490C2213yes—
134#2490C2213yes—
135#2485C2213yes—
136#2485C2213yes—
137#2477C2216yes—
138#2470C2216yes—
139#2468C2213yes—
140#2468C2213yes—
141#2465C2213yes—
142#2465C2213yes—
143#2461C2213yes—
144#2461C2216yes—
145#2461C2213yes—
146#2458C2213yes—
147#2458C2213yes—
148#2454C2213yes—
149#2454C2213yes—
150#2452C2213yes—
151#2452C2213yes—
152#2452C2213yes—
153#2452C2213yes—
154#2445C2213yes—
155#2445C2213yes—
156#2445C2213yes—
157#2445C2213yes—
158#2442C2213yes—
159#2441C2213yes—
160#2440C2213yes—
161#2439C2213yes—
162#2439C2213yes—
163#2439C2213yes—
164#2428C2213yes—
165#2428C2213yes—
166#2426C2216yes—
167#2422C2213yes—
168#2422C2213yes—
169#2420C2213yes—
170#2420C2213yes—
171#2416C2213yes—
172#2416C2213yes—
173#2399C2213yes—
174#2398C2213yes—
175#2396C2213yes—
176#2392C2213yes—
177#2370C2213yes—
178#2370C2213yes—
179#2366C2213yes—
180#2365C2213yes—
181#2363C2213yes—
182#2363C2213yes—
183#2357C2213yes—
184#2355C2213yes—
185#2354C2213yes—
186#2354C2213yes—
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197#2345C2213yes—
198#2344C2213yes—
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2337C2216yes—
212#2335C2216yes—
213#2324C2216yes—
214#2319C2213yes—
215#2314C2213yes—
216C4×C4⋊Q8C2213yes—
217C4×#127C2213yes—
218C4×#125C2213yes—
219C4×#125C2213yes—
220C4×#126C2213yes—
221C4×#126C2213yes—
222C4×#124C2213yes—
223C4×#124C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×#123C2213yes—
227C4×#123C2213yes—
228C4×#121C2213yes—
229C4×#121C2213yes—
230#2298C2213yes—
231#2293C2213yes—
232#2276C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2213yes—
237C42×D4C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241Q82—44no—
242#557—28no—
243#557—44no—
244#550—28no—
245#550—44no—
246#550—44no—
247#542—424no—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2316yes—
254C2×#127C2313yes—
255C2×#127C2313yes—
256C2×#127C2313yes—
257C2×#126C2313yes—
258C2×#126C2313yes—
259C2×#126C2316yes—
260C2×#126C2316yes—
261C2×#125C2313yes—
262C2×#125C2313yes—
263C2×#125C2313yes—
264C2×#125C2313yes—
265C2×#124C2316yes—
266C2×#124C2313yes—
267C2×#124C2316yes—
268C2×#124C2316yes—
269C2×#124C2313yes—
270C2×#124C2316yes—
271C2×#123C2313yes—
272C2×#123C2316yes—
273C2×#123C2316yes—
274C2×#123C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2316yes—
277C2×C22⋊Q8C2313yes—
278C2×C22⋊Q8C2316yes—
279C2×#121C2313yes—
280C2×#121C2313yes—
281C2×#121C2316yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2316yes—
287#520—28no—
288C4×#41—44no—
289C4×#41—44no—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2313yes—
303C2×C4×Q8C2313yes—
304C2×C4×Q8C2313yes—
305C2×C4×Q8C2313yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2316yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×#117C2313yes—
320C2×#117C2316yes—
321C2×#117C2313yes—
322C2×#117C2313yes—
323C22×C4⋊C4C2313yes—
324C22×C42C2313yes—
325C22×C42C2313yes—
326#400C2313yes—
327#400C2316yes—
328#400C2316yes—
329#400C2313yes—
330#400C2311yescharacteristic
331#399C2316yes—
332#399C2313yes—
333#398C2313yes—
334#398C2313yes—
335#398C2316yes—
336#398C2316yes—
337#398C2313yes—
338#398C2311yescharacteristic
339#398C2311yescharacteristic
340#398C2313yes—
341#398C2313yes—
342#397C2316yes—
343#397C2316yes—
344#397C2316yes—
345#397C2316yes—
346#397C2316yes—
347#397C2316yes—
348#397C2316yes—
349#397C2313yes—
350#397C2316yes—
351#397C2313yes—
352#397C2313yes—
353#396C2313yes—
354#396C2316yes—
355#396C2316yes—
356#396C2316yes—
357#396C2316yes—
358#396C2316yes—
359#396C2316yes—
360#396C2316yes—
361#396C2313yes—
362#396C2313yes—
363#396C2313yes—
364#396C2316yes—
365#395C2316yes—
366#395C2313yes—
367#395C2316yes—
368#395C2313yes—
369#395C2311yescharacteristic
370#395C2313yes—
371#395C2313yes—
372#394C2316yes—
373#394C2313yes—
374#394C2316yes—
375#394C2316yes—
376#394C2316yes—
377#394C2316yes—
378#394C2313yes—
379#394C2316yes—
380#394C2316yes—
381#394C2316yes—
382#394C2316yes—
383#394C2316yes—
384#394C2313yes—
385#394C2313yes—
386#394C2313yes—
387#394C2316yes—
388#394C2316yes—
389#394C2316yes—
390#394C2316yes—
391#393C2316yes—
392#393C2316yes—
393#393C2316yes—
394#393C2316yes—
395#393C2316yes—
396#393C2313yes—
397#393C2313yes—
398#393C2313yes—
399#392C2316yes—
400#392C2316yes—
401#392C2313yes—
402#391C2316yes—
403#391C2316yes—
404#391C2316yes—
405#391C2313yes—
406#391C2313yes—
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#390C2316yes—
410#390C2313yes—
411#390C2313yes—
412#390C2316yes—
413#390C2316yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2316yes—
423#390C2316yes—
424#390C2313yes—
425#390C2313yes—
426#390C2316yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#390C2313yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2316yes—
448#389C2313yes—
449#389C2313yes—
450#389C2316yes—
451#389C2316yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#388C2313yes—
467#388C2313yes—
468#388C2313yes—
469#388C2313yes—
470#388C2313yes—
471#388C2313yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#388C2316yes—
476#388C2313yes—
477#388C2316yes—
478#388C2316yes—
479#388C2313yes—
480#388C2316yes—
481#388C2316yes—
482#388C2313yes—
483#388C2316yes—
484#388C2316yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2316yes—
489#388C2316yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2313yes—
497#388C2313yes—
498#388C2313yes—
499#388C2313yes—
500#387C2311yescharacteristic
501#387C2311yescharacteristic
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2313yes—
511#387C2316yes—
512#387C2316yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2311yescharacteristic
519#387C2313yes—
520#387C2311yescharacteristic
521#387C2313yes—
522#387C2311yescharacteristic
523#387C2311yescharacteristic
524#386C2313yes—
525#386C2316yes—
526#386C2316yes—
527#386C2316yes—
528#386C2316yes—
529#386C2316yes—
530#386C2316yes—
531#386C2313yes—
532#385C2313yes—
533#385C2316yes—
534#385C2316yes—
535#385C2316yes—
536#385C2313yes—
537#385C2316yes—
538#385C2313yes—
539#385C2313yes—
540#385C2313yes—
541#385C2313yes—
542#384C2313yes—
543#384C2313yes—
544#384C2313yes—
545#384C2313yes—
546#384C2313yes—
547#383C2313yes—
548#383C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2313yes—
554#382C2313yes—
555#382C2311yescharacteristic
556#381C2316yes—
557#381C2313yes—
558#381C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2316yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2316yes—
570#380C2316yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2316yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2311yescharacteristic
606C4×C4⋊C4C2311yescharacteristic
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624#376C2313yes—
625C43C2313yes—
626C43C2313yes—
627C43C2313yes—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C22×Q8C2411yescharacteristic
638C22×Q8C2413yes—
639C22×Q8C2413yes—
640C22×Q8C2416yes—
641C22×Q8C2411yescharacteristic
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2413yes—
645C22×D4C2413yes—
646C22×D4C2416yes—
647C22×D4C2413yes—
648C22×D4C2413yes—
649C22×D4C2416yes—
650C22×D4C2416yes—
651C23×C4C2413yes—
652C23×C4C2413yes—
653C23×C4C2413yes—
654C23×C4C2416yes—
655C23×C4C2413yes—
656C23×C4C2413yes—
657C23×C4C2413yes—
658C23×C4C2413yes—
659C4⋊Q8—212no—
660C4⋊Q8—46no—
661C4⋊Q8—46no—
662C4⋊Q8—46no—
663C4⋊Q8—46no—
664C4⋊Q8—412no—
665#127—212no—
666#127—46no—
667#127—46no—
668#126—46no—
669#126—412no—
670#126—412no—
671#126—46no—
672#125—212no—
673#125—212no—
674#125—46no—
675#125—46no—
676#124—46no—
677#124—412no—
678#124—412no—
679#124—412no—
680#124—46no—
681#124—412no—
682#123—212no—
683#123—412no—
684#123—412no—
685#123—46no—
686C22⋊Q8—212no—
687C22⋊Q8—46no—
688C22⋊Q8—412no—
689C22⋊Q8—412no—
690#121—212no—
691#121—212no—
692#121—412no—
693#121—412no—
694#121—46no—
695#121—46no—
696#121—46no—
697#121—46no—
698C4×Q8—24no—
699C4×Q8—24no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—212no—
710C4×Q8—212no—
711C4×Q8—46no—
712C4×Q8—46no—
713C4×Q8—46no—
714C4×Q8#4118yes—
715C4×D4—212no—
716C4×D4—212no—
717C4×D4—212no—
718C4×D4—46no—
719C4×D4—46no—
720C4×D4—46no—
721C4×D4—46no—
722C4×D4—46no—
723C4×D4—412no—
724C4×D4—46no—
725C4×D4—46no—
726C4×D4—46no—
727#117—212no—
728#117—412no—
729#117—46no—
730#117—46no—
731C2×C4⋊C4—212no—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2416yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2416yes—
779C2×C4⋊C4C2416yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2416yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2416yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2416yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2416yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2416yes—
826C2×C22⋊C4C2416yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C42—46no—
832C2×C42—46no—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2411yescharacteristic
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2411yescharacteristic
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2411yescharacteristic
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2416yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2413yes—
857C2×C42C2413yes—
858C2×C42C2413yes—
859C2×C42C2411yescharacteristic
860C2×C42C2411yescharacteristic
861C2×C42C2413yes—
862#95C2411yescharacteristic
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2411yescharacteristic
870#95C2411yescharacteristic
871#95C2411yescharacteristic
872#95C2411yescharacteristic
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2411yescharacteristic
877#95C2411yescharacteristic
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2416yes—
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2413yes—
898#95C2413yes—
899#95C2416yes—
900#95C2413yes—
901#95C2411yescharacteristic
902#95C2413yes—
903#95C2411yescharacteristic
904#95C2416yes—
905#95C2416yes—
906#95C2413yes—
907#95C2413yes—
908#95C2416yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2416yes—
914#95C2413yes—
915#95C2413yes—
916#95C2416yes—
917#95C2416yes—
918C24C2513yes—
919C24C2513yes—
920C24C2513yes—
921#41—416no—
922#41—416no—
923#41—416no—
924C2×Q8—26no—
925C2×Q8—26no—
926C2×Q8—26no—
927C2×Q8—22no—
928C2×Q8—22no—
929C2×Q8—41no—
930C2×Q8—43no—
931C2×Q8—43no—
932C2×Q8—43no—
933C2×Q8—46no—
934C2×Q8—46no—
935C2×Q8—46no—
936C2×Q8C2×#4114yes—
937C2×Q8H(5,𝔽2)14yes—
938C2×Q82−1+414yes—
939C2×D4—26no—
940C2×D4—26no—
941C2×D4—26no—
942C2×D4—26no—
943C2×D4—212no—
944C2×D4—26no—
945C2×D4—26no—
946C2×D4—26no—
947C2×D4—26no—
948C2×D4—26no—
949C2×D4—26no—
950C2×D4—26no—
951C2×D4—26no—
952C2×D4—43no—
953C2×D4—43no—
954C2×D4—46no—
955C2×D4—43no—
956C2×D4—43no—
957C2×D4—46no—
958C2×D4—43no—
959C2×D4—43no—
960C2×D4—46no—
961C2×D4—46no—
962C2×D4—46no—
963C2×D4—46no—
964C2×D4—46no—
965C2×D4—46no—
966C22×C4—26no—
967C22×C4—26no—
968C22×C4—26no—
969C22×C4—26no—
970C22×C4—26no—
971C22×C4—26no—
972C22×C4—26no—
973C22×C4—26no—
974C22×C4—26no—
975C22×C4—212no—
976C22×C4—26no—
977C22×C4—26no—
978C22×C4—26no—
979C22×C4—43no—
980C22×C4—43no—
981C22×C4—43no—
982C22×C4—43no—
983C22×C4—46no—
984C22×C4—43no—
985C22×C4—43no—
986C22×C4—43no—
987C22×C4—46no—
988C22×C4—43no—
989C22×C4—43no—
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C22×C4C2513yes—
997C22×C4C2513yes—
998C22×C4C2511yescharacteristic
999C22×C4C2513yes—
1000C22×C4C2513yes—
1001C22×C4C2513yes—
1002C22×C4C2513yes—
1003C22×C4C2513yes—
1004C22×C4C2513yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2513yes—
1007C22×C4C2513yes—
1008C22×C4C2513yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2513yes—
1011C22×C4C2511yescharacteristic
1012C22×C4C2511yescharacteristic
1013C22×C4C2511yescharacteristic
1014C22×C4C2511yescharacteristic
1015C22×C4C2511yescharacteristic
1016C22×C4C2511yescharacteristic
1017C22×C4C2513yes—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—26no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—212no—
1028C4⋊C4—26no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—26no—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—26no—
1041C4⋊C4—22no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—22no—
1045C4⋊C4—26no—
1046C4⋊C4—22no—
1047C4⋊C4—22no—
1048C4⋊C4—46no—
1049C4⋊C4—43no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—46no—
1053C4⋊C4—43no—
1054C4⋊C4—41no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—46no—
1063C4⋊C4—46no—
1064C4⋊C4—46no—
1065C4⋊C4—46no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4C2×#41112yes—
1070C4⋊C4H(5,𝔽2)14yes—
1071C22⋊C4—26no—
1072C22⋊C4—26no—
1073C22⋊C4—26no—
1074C22⋊C4—26no—
1075C22⋊C4—26no—
1076C22⋊C4—26no—
1077C22⋊C4—26no—
1078C22⋊C4—26no—
1079C22⋊C4—26no—
1080C22⋊C4—26no—
1081C22⋊C4—26no—
1082C22⋊C4—26no—
1083C22⋊C4—26no—
1084C22⋊C4—26no—
1085C22⋊C4—26no—
1086C22⋊C4—46no—
1087C22⋊C4—46no—
1088C22⋊C4—46no—
1089C22⋊C4—43no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—43no—
1094C22⋊C4—46no—
1095C22⋊C4—46no—
1096C22⋊C4—46no—
1097C22⋊C4—46no—
1098C22⋊C4—43no—
1099C22⋊C4—46no—
1100C22⋊C4—46no—
1101C22⋊C4—46no—
1102C22⋊C4—43no—
1103C22⋊C4—43no—
1104C22⋊C4—46no—
1105C22⋊C4—43no—
1106C22⋊C4—46no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—46no—
1110C22⋊C4—46no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—43no—
1114C22⋊C4—43no—
1115C22⋊C4—43no—
1116C22⋊C4—43no—
1117C42—26no—
1118C42—26no—
1119C42—26no—
1120C42—26no—
1121C42—26no—
1122C42—26no—
1123C42—26no—
1124C42—26no—
1125C42—26no—
1126C42—26no—
1127C42—26no—
1128C42—26no—
1129C42—26no—
1130C42—26no—
1131C42—22no—
1132C42—22no—
1133C42—22no—
1134C42—26no—
1135C42—41no—
1136C42—41no—
1137C42—43no—
1138C42—43no—
1139C42—46no—
1140C42—43no—
1141C42—43no—
1142C42—43no—
1143C42—43no—
1144C42—43no—
1145C42C2×#41112yes—
1146C23—23no—
1147C23—23no—
1148C23—23no—
1149C23—23no—
1150C23—23no—
1151C23—23no—
1152C23—23no—
1153C23—23no—
1154C23—23no—
1155C23—23no—
1156C23—23no—
1157C23—23no—
1158C23—23no—
1159C23—23no—
1160C23—23no—
1161C23—23no—
1162C23—23no—
1163C23—23no—
1164C23—23no—
1165C23—23no—
1166C23—23no—
1167C23C2611yescharacteristic
1168Q8—44no—
1169Q8—412no—
1170Q8—86no—
1171Q8—166no—
1172Q8#542116yescomplemented
1173D4—412no—
1174D4—412no—
1175D4—412no—
1176D4—412no—
1177D4—86no—
1178D4—86no—
1179D4—812no—
1180D4—166no—
1181D4—166no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—23no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—23no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—21no—
1224C2×C4—23no—
1225C2×C4—21no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—23no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—412no—
1256C2×C4—412no—
1257C2×C4—412no—
1258C2×C4—86no—
1259C2×C4—86no—
1260C2×C4—86no—
1261C2×C4—812no—
1262C2×C4—86no—
1263C2×C4C22×#4112yes—
1264C2×C4C22×#4116yes—
1265C2×C4C22×#4116yes—
1266C2×C4C2×H(5,𝔽2)12yes—
1267C2×C4C2×H(5,𝔽2)12yes—
1268C2×C4C2×H(5,𝔽2)12yes—
1269C2×C4C2×H(5,𝔽2)16yes—
1270C2×C4C2×2−1+416yes—
1271C2×C4#58512yes—
1272C2×C4#58512yes—
1273C2×C4#58512yes—
1274C22—43no—
1275C22—43no—
1276C22—43no—
1277C22—43no—
1278C22—43no—
1279C22—43no—
1280C22—43no—
1281C22—43no—
1282C22—43no—
1283C22—43no—
1284C22—43no—
1285C22—43no—
1286C22—43no—
1287C22—43no—
1288C22—43no—
1289C22—43no—
1290C22—43no—
1291C22—43no—
1292C22—43no—
1293C22—43no—
1294C22—43no—
1295C22C23×#4111yescharacteristic
1296C22C22×H(5,𝔽2)11yescharacteristic
1297C22C22×H(5,𝔽2)11yescharacteristic
1298C22C22×2−1+411yescharacteristic
1299C22C2×#58511yescharacteristic
1300C22C2×#58511yescharacteristic
1301C22C2×#58511yescharacteristic
1302C4—22no—
1303C4—22no—
1304C4—22no—
1305C4—22no—
1306C4—22no—
1307C4—22no—
1308C4—26no—
1309C4—22no—
1310C4—43no—
1311C4—43no—
1312C4—43no—
1313C4—43no—
1314C4—43no—
1315C4—41no—
1316C4—43no—
1317C4—41no—
1318C4—41no—
1319C4—43no—
1320C4—43no—
1321C4—41no—
1322C4—41no—
1323C4—43no—
1324C4—43no—
1325C4—43no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4C2×#542112yes—
1330C2—83no—
1331C2—83no—
1332C2—83no—
1333C2C22×#54211yescharacteristic
1334C2#6279311yescharacteristic
1335C2#6280011yescharacteristic
1336C2#6301411yescharacteristic
1337C2#6302011yescharacteristic
1338C2#6303311yescharacteristic
1339C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36029C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42694C2semidirect
2. #42660C2semidirect
3. #42524C2semidirect
4. #42467C2semidirect
5. #40188C2semidirect
6. #40174C2semidirect
7. #40171C2semidirect
8. #40121C2semidirect
9. #39789C2semidirect
10. #39411C2semidirect
11. #39403C2semidirect
12. #39240C2semidirect
13. #37591C2semidirect
14. #36583C2semidirect
15. #36458C2semidirect
16. #36458C2semidirect
17. #36457C2semidirect
18. #36456C2semidirect
19. #36433C2semidirect
20. #36433C2semidirect
21. #36431C2semidirect
22. #36049C2semidirect
24. #35937C2semidirect
25. #35816C2semidirect
26. #35198C2semidirect
27. #35107C2semidirect
28. #34968C2semidirect
29. #34263C2semidirect
30. C4×#557C2semidirect
31. C4×#550C2semidirect
1172. Q8#542semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#426942
#426602
#425242
#424672
#401882
#401742
#401712
#401212
#397892
#394112
#394032
#392402
#375912
#365832
#364582
#364572
#364562
#364332
#364312
#360492
#360292
#359372
#358162
#351982
#351072
#349682
#342632
C4×#5572
C4×#5502